The present invention relates to magnetic field measurement methods, magnetic field measurement apparatus, magnetic field display methods and magnetic field display apparatus. More particularly the present invention relates to methods and apparatus for measuring magnetic flux at a plurality of points which correspond to two dimensional grids using plural flux meters including superconducting quantum interference devices (hereinafter referred to as SQUID flux meters), for interpolating magnetic flux between the measured points based on the measured magnetic flux and for displaying the measured and interpolated magnetic flux when the display is required.
It is known that a SQUID has a characteristic capable of detecting magnetic flux with extremely high sensitivity. With attention to this characteristic, a SQUID is applied to various apparatus which are used in various technical fields.
When measuring biological magnetic fields with the SQUID, magnetic flux values at plural points which exist in a predetermined plane are measured by using plural SQUID flux meters, then magnetic flux values at all points within the plane are obtained by performing interpolation processings based on the measured magnetic flux, the interpolation processings being linear interpolation processings, spline interpolation processings or least square processings by least square method. Thereafter, after-treatment such as arrow-map display, analysis of magnetic sources and the like is performed based on the magnetic flux at all points thus obtained.
The linear interpolation processings have advantages such as lesser calculation load and higher processing speed. But the linear interpolation processings have disadvantages such that interpolation results between the measured points are decreased in accuracy and isomagnetic contour lines are displayed as kinked lines when the display is required. The linear interpolation processings have a further disadvantage that applicable usage is limited to cases which do not need arrow-map display because partial differential values cannot be obtained based on interpolation results obtained by linear interpolation processings, the partial differential values being necessary for arrow-map display.
The interpolation processings using spline interpolation or least square method can eliminate the above-mentioned disadvantages of the linear interpolation processings because the interpolation processings using spline interpolation or least square method can interpolate a curved surface. The interpolation processings using spline interpolation or least square method have disadvantages such that the calculation load is remarkably increased more than the linear interpolation processings, real time magnetic field measurement and real time magnetic field display are impossible to perform. More specifically, a computer which has a large capacity and high processing speed is needed because calculation load is remarkably increased. And real time magnetic field measurement and real time magnetic field display are impossible to perform even when a computer having a large capacity and high processing speed is employed. Furthermore, when partial differential values which are necessary for arrow-map display, are to be calculated, magnetic flux should be obtained by interpolation processings, then partial differential values should be calculated based on the obtained magnetic flux by numerical differential method, thereby the necessary time period for obtaining partial differential values is lengthened remarkably.